{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QGUME7TDDC3UVWG54CN4HNGK3M","short_pith_number":"pith:QGUME7TD","canonical_record":{"source":{"id":"1611.07628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-23T03:27:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9d2beec877bb96f09a71b4e1e0e26f4486b4f560898650643d5f38fe9d3e58ea","abstract_canon_sha256":"003e4a062f3b19cabf9ace7ec21df54d6b152570b56a196ae680d11589d1af27"},"schema_version":"1.0"},"canonical_sha256":"81a8c27e6318b74ad8dde09bc3b4cadb0a634ec5bbaa5a277f678c82cc2702ac","source":{"kind":"arxiv","id":"1611.07628","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07628","created_at":"2026-05-18T00:33:22Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07628v2","created_at":"2026-05-18T00:33:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07628","created_at":"2026-05-18T00:33:22Z"},{"alias_kind":"pith_short_12","alias_value":"QGUME7TDDC3U","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QGUME7TDDC3UVWG5","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QGUME7TD","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QGUME7TDDC3UVWG54CN4HNGK3M","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07628","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-23T03:27:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9d2beec877bb96f09a71b4e1e0e26f4486b4f560898650643d5f38fe9d3e58ea","abstract_canon_sha256":"003e4a062f3b19cabf9ace7ec21df54d6b152570b56a196ae680d11589d1af27"},"schema_version":"1.0"},"canonical_sha256":"81a8c27e6318b74ad8dde09bc3b4cadb0a634ec5bbaa5a277f678c82cc2702ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:22.292533Z","signature_b64":"xGO4K2OyWbwIR7fWgn3XfTBuEswg3HY0xFy+LN7dPFU8bbkSadGJ2jpsnHRpWwIFnXdSAT/WkbCcevlcXtnnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81a8c27e6318b74ad8dde09bc3b4cadb0a634ec5bbaa5a277f678c82cc2702ac","last_reissued_at":"2026-05-18T00:33:22.291952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:22.291952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07628","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p0rqgvHFDZ5783chC2u6NJTmlXpAY9EzH8/NJZU0fwg7cfW0ZZu9YIgjXf59GHQComeIHkr+7NbcbqH7v4wABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:20:09.333388Z"},"content_sha256":"91723dc5555c59816479de4771dcea4ccc0005312d3964a2685f5a34a65392af","schema_version":"1.0","event_id":"sha256:91723dc5555c59816479de4771dcea4ccc0005312d3964a2685f5a34a65392af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QGUME7TDDC3UVWG54CN4HNGK3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nearly Optimal Bounds for Orthogonal Least Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jian Wang, Jinming Wen, Qinyu Zhang","submitted_at":"2016-11-23T03:27:58Z","abstract_excerpt":"In this paper, we study the orthogonal least squares (OLS) algorithm for sparse recovery. On the one hand, we show that if the sampling matrix $\\mathbf{A}$ satisfies the restricted isometry property (RIP) of order $K + 1$ with isometry constant $$ \\delta_{K + 1} < \\frac{1}{\\sqrt{K+1}}, $$ then OLS exactly recovers the support of any $K$-sparse vector $\\mathbf{x}$ from its samples $\\mathbf{y} = \\mathbf{A} \\mathbf{x}$ in $K$ iterations. On the other hand, we show that OLS may not be able to recover the support of a $K$-sparse vector $\\mathbf{x}$ in $K$ iterations for some $K$ if $$ \\delta_{K + 1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07628","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IOHJZa8/8tfm8mqBafiAgPwdWukDa2ofT1WX87owEnL/NBg80gkL4OngPn9ITtk0iohVJnorHJZqU1n9U7R8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:20:09.333748Z"},"content_sha256":"0226fa0a1b98a1e58a369cab204dc7e5608758ddcb9c9339be673840b0997b55","schema_version":"1.0","event_id":"sha256:0226fa0a1b98a1e58a369cab204dc7e5608758ddcb9c9339be673840b0997b55"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QGUME7TDDC3UVWG54CN4HNGK3M/bundle.json","state_url":"https://pith.science/pith/QGUME7TDDC3UVWG54CN4HNGK3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QGUME7TDDC3UVWG54CN4HNGK3M/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T03:20:09Z","links":{"resolver":"https://pith.science/pith/QGUME7TDDC3UVWG54CN4HNGK3M","bundle":"https://pith.science/pith/QGUME7TDDC3UVWG54CN4HNGK3M/bundle.json","state":"https://pith.science/pith/QGUME7TDDC3UVWG54CN4HNGK3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QGUME7TDDC3UVWG54CN4HNGK3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QGUME7TDDC3UVWG54CN4HNGK3M","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"003e4a062f3b19cabf9ace7ec21df54d6b152570b56a196ae680d11589d1af27","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-23T03:27:58Z","title_canon_sha256":"9d2beec877bb96f09a71b4e1e0e26f4486b4f560898650643d5f38fe9d3e58ea"},"schema_version":"1.0","source":{"id":"1611.07628","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07628","created_at":"2026-05-18T00:33:22Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07628v2","created_at":"2026-05-18T00:33:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07628","created_at":"2026-05-18T00:33:22Z"},{"alias_kind":"pith_short_12","alias_value":"QGUME7TDDC3U","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QGUME7TDDC3UVWG5","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QGUME7TD","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:0226fa0a1b98a1e58a369cab204dc7e5608758ddcb9c9339be673840b0997b55","target":"graph","created_at":"2026-05-18T00:33:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study the orthogonal least squares (OLS) algorithm for sparse recovery. On the one hand, we show that if the sampling matrix $\\mathbf{A}$ satisfies the restricted isometry property (RIP) of order $K + 1$ with isometry constant $$ \\delta_{K + 1} < \\frac{1}{\\sqrt{K+1}}, $$ then OLS exactly recovers the support of any $K$-sparse vector $\\mathbf{x}$ from its samples $\\mathbf{y} = \\mathbf{A} \\mathbf{x}$ in $K$ iterations. On the other hand, we show that OLS may not be able to recover the support of a $K$-sparse vector $\\mathbf{x}$ in $K$ iterations for some $K$ if $$ \\delta_{K + 1","authors_text":"Jian Wang, Jinming Wen, Qinyu Zhang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-23T03:27:58Z","title":"Nearly Optimal Bounds for Orthogonal Least Squares"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07628","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:91723dc5555c59816479de4771dcea4ccc0005312d3964a2685f5a34a65392af","target":"record","created_at":"2026-05-18T00:33:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"003e4a062f3b19cabf9ace7ec21df54d6b152570b56a196ae680d11589d1af27","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-11-23T03:27:58Z","title_canon_sha256":"9d2beec877bb96f09a71b4e1e0e26f4486b4f560898650643d5f38fe9d3e58ea"},"schema_version":"1.0","source":{"id":"1611.07628","kind":"arxiv","version":2}},"canonical_sha256":"81a8c27e6318b74ad8dde09bc3b4cadb0a634ec5bbaa5a277f678c82cc2702ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81a8c27e6318b74ad8dde09bc3b4cadb0a634ec5bbaa5a277f678c82cc2702ac","first_computed_at":"2026-05-18T00:33:22.291952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:22.291952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xGO4K2OyWbwIR7fWgn3XfTBuEswg3HY0xFy+LN7dPFU8bbkSadGJ2jpsnHRpWwIFnXdSAT/WkbCcevlcXtnnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:22.292533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07628","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91723dc5555c59816479de4771dcea4ccc0005312d3964a2685f5a34a65392af","sha256:0226fa0a1b98a1e58a369cab204dc7e5608758ddcb9c9339be673840b0997b55"],"state_sha256":"16cff51594fa3466f07ffbcf0ef7d1a3e64cdcbd4e209c0b2e7a9e806331ae74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MuC4wKWNrY3jJkqEmeQaEgdbG8QMmPz7pmYyDU1jQp21urtCHgv2Tvi5N3V9yLj5ZEKi6TDruxhb69CVeygYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:20:09.335625Z","bundle_sha256":"9f7723dc7f29ed07f6a66533e035b09ab6bf7659ad2a9a36fa0e9bf332b5126d"}}